Related papers: Renormalisation of Fermionic Cellular Automata
Any algorithm (in the sense of Gurevich's abstract-state-machine axiomatization of classical algorithms) operating over any arbitrary unordered domain can be simulated by a dynamic cellular automaton, that is, by a pattern-directed cellular…
We study the solutions of the interacting Fermionic cellular automaton introduced in Ref. [Phys Rev A 97, 032132 (2018)]. The automaton is the analogue of the Thirring model with both space and time discrete. We present a derivation of the…
Several cellular automata (CA) models have been developed to simulate self-organization of multiple levels of structures. However, they do not obey microscopic reversibility and conservation laws. In this paper, we describe the construction…
A map on finitely many fermionic modes represents a unitary evolution if and only if it preserves canonical anti-commutation relations. We use this condition for the classification of fermionic cellu- lar automata (FCA) on Cayley graphs of…
We present a preliminary results of our Galactic Habitable Zone (GHZ) 2D probabilistic cellular automata models. The relevant time-scales (emergence of life, it's diversification and evolution influenced with the global risk function) are…
We study two-dimensional cellular automata, each cell takes three states: resting, excited and refractory. A resting cell excites if number of excited neighbours lies in a certain interval (excitation interval). An excited cell become…
We study the renormalization group behaviour of the topological charge density in full QCD on the lattice. We propose a way of extracting the necessary renormalization functions from Monte Carlo simulations.
This investigation studies the ergodic properties of reversible linear cellular automata over $\mathbb{Z}_m$ for $m \in \mathbb{N}$. We show that a reversible linear cellular automaton is either a Bernoulli automorphism or non-ergodic. This…
We show that a behaviour analogous to degenerate hyperbolicity can occur in nearest-neighbour cellular automata (CA) with three states. We construct a 3-state rule by "lifting" elementary CA rule 140. Such "lifted" rule is equivalent to…
A Quantum Cellular Automaton (QCA) is essentially an operator driving the evolution of particles on a lattice, through local unitaries. Because $\Delta_t=\Delta_x = \epsilon$, QCAs constitute a privileged framework to cast the digital…
We build the two dimensional Gross-Neveu model by a new method which requires neither cluster expansion nor discretization of phase-space. It simply reorganizes the perturbative series in terms of trees. With this method we can for the…
We propose a scheme for constructing classical spin Hamiltonians from Hunds coupled spin-fermion models in the limit J_H/t \to \infinity. The strong coupling between fermions and the core spins requires self-consistent calculation of the…
This paper explores the algebraic conditions under which a cellular automaton with a non-linear local rule exhibits surjectivity and reversibility. We also analyze the role of permutivity as a key factor influencing these properties and…
We construct a hierarchy of lattice fermions, where the coarser lattice Dirac operator is the Schur complement of the block UL decomposition of the finer lattice operator. We show that the construction is an exact gauged renormalisation…
There exists algorithms to detect reversibility of cellular automaton (CA) for both finite and infinite lattices taking quadratic time. But, can we identify a $d$-state CA rule in constant time that is always reversible for every lattice…
We define a family of Schroedinger Functional renormalization schemes for the four-quark multiplicatively renormalizable operators of the $\Delta F = 1$ and $\Delta F = 2$ effective weak Hamiltonians. Using the lattice regularization with…
We present a hybrid numerical approach to simulate quantum many body problems on two spatial dimensional quantum lattice models via the non-Abelian ab initio version of the density matrix renormalization group method on state-of-the-art…
Recursive equations for the number of cells with nonzero values at $n$-th step for some two-dimensional reversible second-order cellular automata are proved in this work. Initial configuration is a single cell with the value one and all…
We study a mixture of ultracold spin-half fermionic and spin-one bosonic atoms in a shallow optical lattice where the bosons are coupled to the fermions via both density-density and spin-spin interactions. We consider the parameter regime…
Universality in cellular automata theory is a central problem studied and developed from their origins by John von Neumann. In this paper, we present an algorithm where any Turing machine can be converted to one-dimensional cellular…